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Motivated by a work of Li, we study nonlocal vertex algebras and their smash products over fields of positive characteristic. Through smash products, modular vertex algebras associated with positive definite even lattices are reconstructed. This gives a different construction of the modular vertex algebras obtained from integral forms introduced by Dong and Griess in lattice vertex operator algebras over a field of characteristic zero. [ABSTRACT FROM AUTHOR]

Background: Accumulating evidence indicates that miRNAs are involved in multiple cellular functions and participate in various cancer development and progression, including breast cancer. Methods: We aimed to investigate the role of miR-381-3p in breast cancer. The expression level of miR-381-3p and EMT transcription factors was examined by quantitative real-time PCR (qRT-PCR). The effects of miR-381-3p on breast cancer proliferation and invasion were determined by Cell Counting Kit-8 (CCK-8), colony formation, and transwell assays. The regulation of miR-381-3p on its targets was determined by dual-luciferase analysis, qRT-PCR, and western blot. Results: We found that the expression of miR-381-3p was significantly decreased in breast cancer tissues and cell lines. Overexpression of miR-381-3p inhibited breast cancer proliferation and invasion, whereas knockdown of miR-381-3p promoted cell proliferation and invasion in MDA-MB-231 and SKBR3 cells. Mechanistically, overexpression of miR-381-3p inhibited breast cancer epithelial–mesenchymal transition (EMT). Both Sox4 and Twist1 were confirmed as targets of miR-381-3p. Moreover, transforming growth factor-β (TGF-β) could reverse the effects of miR-381-3p on breast cancer progression. Conclusions: Our observation suggests that miR-381-3p inhibits breast cancer progression and EMT by regulating the TGF-β signaling via targeting Sox4 and Twist1. [ABSTRACT FROM AUTHOR]

Onboard cable is important electrical equipment of an electric locomotive. In order to effectively evaluate the aging state of the cable, this article proposes a method to evaluate the aging state of the cable based on a new method of dielectric spectrum data processing and a new structure model of recognition algorithm. First, the log-min-max gray-scale (LMMGS) method is proposed, which transforms the dielectric parameters based on the frequency-domain dielectric spectrum (FDS) test into the gray matrix. The correlation among different dielectric parameters is retained, and the interference of their order of magnitude difference on feature extraction is reduced. Then, the new structure of spatial pyramid pooling (SPP) is improved by rectangular mesh dividing named Rectangular-SPP, which increases the number of divisible layers of the spatial pyramid, and it is used to optimize convolutional neural network (CNN), so as to remove the limitation of recognition algorithm on the size of input data and expand the scale of feature extraction. Finally, a set of methods for evaluating the aging state of onboard cable is proposed. The experimental results show that this method can effectively distinguish the insulation aging state of onboard cable. Meanwhile, the proposed Rectangular-SPP-CNN algorithm has a better performance than the conventional machine learning algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we continue previous studies on quasimodules at infinity for (weak) quantum vertex algebras, focusing on equivariant quasimodules at infinity for vertex Γ-algebras. Among the main results, we obtain a commutator formula and certain general conceptual results. As an application, we establish a category equivalence between the category of lowest weight modules for a certain family of Lie algebras and the category of equivariant quasimodules at infinity for a certain family of vertex Γ-algebras. [ABSTRACT FROM AUTHOR]

We report a systematic study of large-scale growth of high-quality WSe2 atomic layers directly on SiO2/Si substrates using a convenient method. Various parameters, especially growth temperatures, flow rate of carrier gas and tube pressure, are investigated in affecting the properties of as-grown WSe2 flakes in terms of their sizes, shapes and thickness. The pre-annealing step is demonstrated to be a key role in achieving the large-scale growth. Under an optimized condition, the lateral size of triangular single-crystal monolayer WSe2 is up to 30 m and the area of the monolayer thin film can be up to 0.25 mm2. And some other interesting features, such as nanoflowers, are observed, which are a promising for catalyzing research. Raman spectrum and microphotoluminescence indicate distinct layer dependent efficiency. Auger electron spectroscopy (AES) studies demonstrate the atomic concentration of the as-grown WSe2. Electrical transport further shows that the -type WSe2 field-effect transistors exhibit excellent electrical properties with carrier mobility of 64 cmVs and current on/off ratio over 105. These results are comparable to the exfoliated materials. [ABSTRACT FROM AUTHOR]

We study class of finite-dimensional Cantan-type Lie superalgebras HO( m) over a field of prime characteristic, which can be regarded as extensions of odd Hamiltonian superalgebra HO. And we also determine the derivation superalgebras of Lie superalgebras HO( m). [ABSTRACT FROM AUTHOR]

The natural filtrations of hamiltonian superalgebras of formal vector fields are proved to be invariant under their automorphism group, by determining the set of ad-quasi-nilpotent elements. Thereby, the automorphism group of these Lie superalgebras are determined. [ABSTRACT FROM AUTHOR]

The Weisfeiler filtrations of infinite-dimensional odd contact superalgebras over fields of positive characteristic are proved to be invariant under automorphisms by characterizing ad-nilpotent elements. Thereby, we are able to obtain an intrinsic characterization of odd contact superalgebras and a property of automorphisms of these Lie superalgebras. [ABSTRACT FROM PUBLISHER]

A class of finite-dimensional Cartan-type Lie superalgebras H(n,m) over a field of prime characteristic is studied in this paper. We first determine the derivation superalgebra of H(n,m). Then we obtain that H(n,m) is restrictable and it is an extension of the Lie superalgebra $\widetilde{H}(n)$. Finally, we prove that H(n,m) is isomorphic to a subalgebra of the restricted Hamiltonian Lie superalgebra $H(n,m,\underline{1})$. [ABSTRACT FROM AUTHOR]

The natural filtration of the infinite-dimensional Hamiltonian Lie superalgebra over a field of positive characteristic is proved to be invariant under automorphisms by characterizing ad-nilpotent elements. We are thereby able to obtain an intrinsic characterization of the Hamiltonian Lie superalgebra and establish a property of the automorphisms of the Lie superalgebra. [ABSTRACT FROM AUTHOR]